Inkjet printing is not an option due to the real-world resolution that could be achieved being very low (<300dpi) added to other optical and ink based fuzz/bleed/dirt etc. Pigment inks are also opaque.

Laser printing is also not an option as the toner is opaque and suffers similar resolution limits.

You have only 2 options that I can think of:

1 - Make the slide bigger - E.G. A4, on inkjet acetate and use an OHP instead of the 35mm equipment quoted (so not a solution to the question)

2 - Do it optically. Get a camera loaded with slide film and a long-ish lens (85-150mm) Take a photo of your monitor displaying each picture (You will probably want to do this with your DSLR first to get the exposure correct) You will want to have it as a fairly long-exposure (> 1/2sec) to negate any oddities caused by backlight/refresh frequency. This is the only method that I can think of that you can do at home that will yield sufficient on-film resolution for display.

Don't worry about trying to attempt colour film development at home, it is complex and expensive -just send your roll off for standard development.

Source: I used to work for Epson.

.... Or just use a digital projector.